I thought this would be phrased as: אני שותה מים מן הכוס שלי. I'm familiar with using the preposition מ combined with a pronoun (like ממני) but is it common to use the the preposition מ with the definite article ה before a noun?? Maybe i just missed that one back in the day :)
Another participant (AdamSomething) explained it thoroughly in another exercise in this lesson. If you missed it, in short - both orders are possible, in all sentences. Typically the thing that comes first after the verb is already known or established in the conversation, and the thing that comes last is what you want to stress.